x^2+20x-420=0

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Solution for x^2+20x-420=0 equation: 


Simplifying
x2 + 20x + -420 = 0

Reorder the terms:
-420 + 20x + x2 = 0

Solving
-420 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '420' to each side of the equation.
-420 + 20x + 420 + x2 = 0 + 420

Reorder the terms:
-420 + 420 + 20x + x2 = 0 + 420

Combine like terms: -420 + 420 = 0
0 + 20x + x2 = 0 + 420
20x + x2 = 0 + 420

Combine like terms: 0 + 420 = 420
20x + x2 = 420

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 420 + 100

Reorder the terms:
100 + 20x + x2 = 420 + 100

Combine like terms: 420 + 100 = 520
100 + 20x + x2 = 520

Factor a perfect square on the left side:
(x + 10)(x + 10) = 520

Calculate the square root of the right side: 22.803508502

Break this problem into two subproblems by setting 
(x + 10) equal to 22.803508502 and -22.803508502.


Subproblem 1
x + 10 = 22.803508502

Simplifying
x + 10 = 22.803508502

Reorder the terms:
10 + x = 22.803508502

Solving
10 + x = 22.803508502

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = 22.803508502 + -10

Combine like terms: 10 + -10 = 0
0 + x = 22.803508502 + -10
x = 22.803508502 + -10

Combine like terms: 22.803508502 + -10 = 12.803508502
x = 12.803508502

Simplifying
x = 12.803508502


Subproblem 2
x + 10 = -22.803508502

Simplifying
x + 10 = -22.803508502

Reorder the terms:
10 + x = -22.803508502

Solving
10 + x = -22.803508502

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = -22.803508502 + -10

Combine like terms: 10 + -10 = 0
0 + x = -22.803508502 + -10
x = -22.803508502 + -10

Combine like terms: -22.803508502 + -10 = -32.803508502
x = -32.803508502

Simplifying
x = -32.803508502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.803508502, -32.803508502}

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